1. Field of the Invention
This invention is related in general to the field of phase-shifting interferometry (PSI) and, in particular, to a novel approach to the solution of the phase-ambiguity problem inherent with PSI measurements.
2. Description of the Related Art
The benefits of optical surface profilometry include the ability to perform non-contact measurements of delicate surfaces, excellent height resolution, and high measurement speed. Among the various techniques that have evolved for optical testing, phase-shifting interferometry is an important tool that is used to obtain fast, three-dimensional profiles of smooth surfaces. It is founded on the basic concept of varying the phase difference between two coherent interfering beams of single wavelength in some known manner, such as by changing the optical path difference (OPD) in discrete steps or linearly with time. Under such conditions, three or more measurements of the light intensity at a pixel of a receiving sensor array can be used to determine the initial phase difference of the light beams at the point on a test surface corresponding to that pixel. Based on such measurements at each pixel of coordinates x and y, a phase distribution map .phi.(x,y) can be determined for the test surface, from which very accurate height data h(x,y) are calculated in relation to the wavelength .lambda. of the light source used by the following general equation: ##EQU1##
Phase-shifting interferometry provides a vertical resolution on the order of 1/100 of a wavelength or better. Therefore, the technique is typically limited to measurements of smooth, polished, homogeneous surfaces.
When measurements of rougher surfaces, or surfaces with dissimilar optical properties, are made, severe errors can arise. As well understood by those skilled in the art, PSI measurements are very precise and the corresponding height calculations are very reliable so long as the surface height varies by incremental steps less than 1/4 of the wavelength .lambda. between adjacent pixels; that is, the phase must not change by more than .pi., or .lambda./2 in the optical path difference, between two adjacent pixels. The phase data are integrated horizontally in conventional fashion by adding or subtracting 2.pi. to ensure that the absolute value of the phase difference between any pair of adjacent pixels is less than .pi.. If large vertical steps exist (corresponding to an inter-pixel height difference greater than one quarter wavelength), phase-integration errors of multiples of 2.pi. in magnitude (known as 2.pi. ambiguities) result in the integrated-phase map .phi.(x,y) generated for the surface and, correspondingly, in the calculated height map h(x,y). Since practical hardware considerations, such as detector array cost and sensitivity, limit the useful range of wavelengths available for phase shifting to about 400 to 700 nm, it is readily apparent that large-step height measurements require additional processing of the raw phase data to remove phase ambiguities between adjacent pixels.
Note that the term horizontal integration is used herein to refer to integration steps taken to correct phase ambiguities between adjacent pixels. On the other hand, the term vertical integration is used to refer to steps taken to correct phase ambiguities present in determining the height of an individual pixel with respect to an approximate value calculated by a coarser procedure.
Because phase shifting allows very accurate measurements with high resolution, which are not attainable by any other known technique, much work has been done to overcome the problem of phase ambiguity in order to utilize the procedure to measure steep surfaces with relatively large inter-pixel step heights. A theoretical technique for overcoming the problem is based on the concept of performing phase shifting with a long wavelength .lambda..sub.L, greater than four times the maximum step to be measured between adjacent pixels, and then repeating the measurements with a relatively shorter wavelength .lambda..sub.S, as needed for the required degree of resolution. Thus, the phase distribution map generated with .lambda..sub.L is free of ambiguities and can be used to establish a coarse map of the relative height of each test-surface area corresponding to a pixel in the sensor array. The finer-resolution measurements generated with .lambda..sub.S are then superimposed over the coarse data to generate a refined map free of 2.pi. ambiguities.
In practice, though, the cost of combining available sensor technology in a single instrument to perform phase shifting with a large spectrum of monochromatic light sources (such as infrared, visible and ultraviolet) is prohibitive for commercial applications. On the other hand, charge-coupled-device (CCD) cells are relatively inexpensive and have become the preferred detector for PSI applications because of their speed of response and accuracy for carrying out on-line measurements of intensity. CCD arrays' typical wavelength range of operation is from approximately 400 nm to about 1,000 nm. Therefore, for the purpose of measuring large steps in surface height, such as inter-pixel discontinuities in the order of 400 nm, which would require coarse measurements with a wavelength greater than 1,600 nm (i.e., in the infrared spectrum), a CCD detector alone is not suitable and the two wavelength technique does not provide a viable solution to the phase ambiguity problem. Therefore, artificial devices need to be utilized to overcome these limitations.
In U.S. Pat. No. 4,832,489 (1989), hereby incorporated by reference, Wyant et al. describe a two-wavelength phase shifting technique wherein two relatively short wavelengths, both within the range of operation of the sensor array, are used in combination to generate phase data corresponding to a synthesized, equivalent, longer wavelength. Thus, a coarse map of the sample surface is produced with such equivalent wavelength and these data are then combined with height measurements derived from single-wavelength phase shifting to produce a corrected height map. While a great improvement over previous procedures used to measure relatively large steps, the two-wavelength technique requires two beams of single-wavelength (quasimonochromatic) light dedicated to phase shifting. In addition, the technique is still limited by the fact that the maximum equivalent wavelength feasible by this technique is only about ten times the length of the longer single wavelength used; if a longer equivalent wavelength is synthesized, the system noise becomes too great for reliable results. Therefore, the maximum surface-height step effectively measurable by this technique is still limited to about 10/4 of the longer wavelength utilized in the procedure. In practice, this constitutes only a ten-fold improvement over single-wavelength phase-shifting and is not adequate for large inter-pixel steps.
Thus, in practice conventional PSI has been limited to measurements of fairly smooth, continuous surfaces; and large-step and steep-surface measurements have been carried out by white-light or broad-bandwidth-light vertical scanning interferometry (VSI), a well-known technique detailed in the prior art (see Caber, Paul J., "Interferometric Profiler for Rough Surfaces," Applied Optics, 32(11):3438-3441, 1993, incorporated herein by reference). As VSI is implemented in the Caber reference, for example, white light is used as the interferometer light source and the degree of fringe modulation, or coherence, of the interference fringes (instead of their phase) produced at the light detector is measured for various distances between a test surface and the reference surface of the interferometer (each distance corresponding to a different optical path difference, OPD) in order to determine surface height. The method typically involves vertical scanning of the reference arm of the interferometer with respect to a stationary sample and calculation of the relative modulation of the intensity signal as a function of vertical position. Such VSI techniques have been used successfully in overcoming the limitations of surface height measurements encountered in conventional phase-shifting interferometry, but are not as precise because of VSI's much lower resolution in comparison to single-wavelength phase shifting.
As vertical scanning interferometry becomes a preferred method for measuring rough surface heights (that is, surfaces with steep gradients or with discontinuities), especially with the expanded range of operation made possible by the motorized translators described in the referenced companion application, it would be very desirable to improve the vertical resolution of the VSI procedure. In addition, because the motorized hardware required for VSI can be combined with phase-shifting hardware, as also demonstrated in the companion application, the concept of combining the two procedures to improve the shortcomings of both appears to be a natural step in the normal evolution of interferometric technology. Therefore, this invention is directed at providing a method and apparatus for combining white-light vertical scanning and phase shifting to make very precise measurements of large steps and steep gradients in the height map of a test surface.